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Discrete orthogonal matrix polynomials

Дискретные ортогональные матричные полиномы

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Abstract

At the present time, the theory of orthogonal matrix polynomials is an active area of mathematics and exhibits a promising future. However, the discrete case has been completely forgotten. In this note we introduce the notion of discrete orthogonal matrix polynomials, and show some algebraic properties. In particular, we study a matrix version of the usual Meixner polynomials.

Резюме

В настояъее время теория ортогональных матричных полиномов является активной областью математики и показывает надежное будуъее. Однако, дискретный случай совсем забыт. В зтой заметке мы вводим понятие дискретных матричных полиномов и покажем их некоторые алгебраические свойства. В частности, мы изучаем один их матричных вариантов привычных полиномов Мейкснера.

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Authors and Affiliations

  1. CIMAT, Callejón Jalisco s/n Mineral de Valenciana, Guanajuato, Gto, México

    Raúl Felipe

  2. ICIMAF, Calle F esquina a 15, No 309, Vedado, Ciudad de la Habana, Cuba

    Raúl Felipe

Authors
  1. Raúl Felipe
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Correspondence to Raúl Felipe.

Additional information

Dedicated to the memory of Miklós Farkas

The author was supported in part under CONACYT Grant 37558E and in part under the Cuba National Project “Theory and algorithms for the solution of problems in algebra and geometry”.

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Felipe, R. Discrete orthogonal matrix polynomials. Anal Math 35, 189–197 (2009). https://doi.org/10.1007/s10476-009-0302-2

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  • DOI: https://doi.org/10.1007/s10476-009-0302-2

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